Example of singular reduction in symplectic diffeology

Abstract

We present an example of symplectic reduction in diffeology where the space involved is infinite dimensional and the reduction is singular. This example is a mix of two cases that are not handled by ordinary symplectic geometry. We show that, in this infinite dimensional example, the singularities are distributed in such a way that the symplectic form, restricted to a generic level of the moment map, passes to the reduced space.